Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
www.hydrol-earth-syst-sci.net/16/3293/2012/
doi:10.5194/hess-16-3293-2012
© Author(s) 2012. CC Attribution 3.0 License.
Hydrology and
Earth System
Sciences
Depression storage and infiltration effects on overland flow
depth-velocity-friction at desert conditions: field plot results and
model
M. J. Rossi and J. O. Ares
National Patagonic Centre, CONICET, Boulvd. Brown 2915, 9120 Puerto Madryn, Chubut, Argentina
Correspondence to: M. J. Rossi ([email protected])
Received: 3 April 2012 – Published in Hydrol. Earth Syst. Sci. Discuss.: 7 May 2012
Revised: 6 August 2012 – Accepted: 20 August 2012 – Published: 14 September 2012
Abstract. Water infiltration and overland flow are relevant in
considering water partition among plant life forms, the sustainability of vegetation and the design of sustainable hydrological models and management. In arid and semi-arid regions, these processes present characteristic trends imposed
by the prevailing physical conditions of the upper soil as
evolved under water-limited climate. A set of plot-scale field
experiments at the semi-arid Patagonian Monte (Argentina)
were performed in order to estimate the effect of depression storage areas and infiltration rates on depths, velocities and friction of overland flows. The micro-relief of undisturbed field plots was characterized at z-scale 1 mm through
close-range stereo-photogrammetry and geo-statistical tools.
The overland flow areas produced by controlled water inflows were video-recorded and the flow velocities were measured with image processing software. Antecedent and postinflow moisture were measured, and texture, bulk density and
physical properties of the upper soil were estimated based
on soil core analyses. Field data were used to calibrate a
physically-based, mass balanced, time explicit model of infiltration and overland flows. Modelling results reproduced
the time series of observed flow areas, velocities and infiltration depths. Estimates of hydrodynamic parameters of overland flow (Reynolds-Froude numbers) are informed. To our
knowledge, the study here presented is novel in combining
several aspects that previous studies do not address simultaneously: (1) overland flow and infiltration parameters were
obtained in undisturbed field conditions; (2) field measurements of overland flow movement were coupled to a detailed
analysis of soil microtopography at 1 mm depth scale; (3)
the effect of depression storage areas in infiltration rates and
depth-velocity friction of overland flows is addressed. Relevance of the results to other similar desert areas is justified
by the accompanying biogeography analysis of similarity of
the environment where this study was performed with other
desert areas of the world.
1
Introduction
The complexity of interactions between overland flow and
infiltration has long received attention in hydrological studies. The spatial variability of soil microtopography has been
identified as a major determinant of infiltration rates and the
hydrological response of watersheds (Abrahams et al., 1990;
Köhne et al., 2009; Darboux et al., 2001). Usual procedures
to study run-off-infiltration processes involve the use of hydrological models based on hydrograph records. Although
a large body of literature has been devoted to the criteria
used to inspect hydrograph records (Ewen, 2011), less attention has been paid to the fact that many hydrological models
that can accurately reproduce hydrograph records, produce
severely biased estimates of overland flow velocities (Mügler
et al., 2011; Legout et al., 2012) or Reynolds-Froude numbers (Tatard et al., 2008).
Infiltration-run-off models need to calculate the overland
flow velocity and depth to be able to simulate the flow of water over the land surface. Frictional effects must be accounted
for, usually through simplifying equations of the fundamental hydrodynamic laws on continuity and momentum balance
involved. To this aim, most field and laboratory studies on
overland flow use the Darcy-Weisbach’s f and Manning’s n
Published by Copernicus Publications on behalf of the European Geosciences Union.
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M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
(Darboux et al., 2001; Hessel et al., 2003; Li, 2009). Both
of these are calculated from the same variables (flow rate,
terrain slope, roughness, Reynolds numbers) and both suffer
from limitations imposed by the high variability of the represented effects both in space and time. Abrahams et al. (1990)
studied Darcy-Weisbach’s f for desert hill slopes and found
that it varies with the rate of flow. Since the rate of flow is
highly variable in space, so too is f . Analogous limitations
can be expected in relation to Manning’s n.
In the case of arid and semi-arid areas, complex interactions between run-off generation, transmission and reinfiltration over short temporal scales (Li et al., 2011; Reaney, 2008) add difficulties in the estimation of infiltrationoverland flows. In these areas, the soil surface is predominantly flat and gently sloped at extended spatial scales, and
the excess rainfall moves at the surface of the soil in very
shallow structures combining small overland flow areas interspersed with finely ramified fingering patterns of small channels. Infiltration in arid and semi-arid regions can also be
modified by the development of water-repellent areas (Lipsius and Mooney, 2006) which in cases occur in relation to
soil microtopography (Biemelt et al., 2005).
Composite patterns of overland flow (Parsons and Wainwright, 2006; Smith et al., 2011) can be expected to produce
spatially heterogeneous patterns of water infiltration in the
upper soil (van Schaik, 2009). Results obtained by Esteves et
al. (2000) in laboratory run-off plots, indicate that despite the
soil being represented by only one set of parameters, infiltration was not homogeneous all over the plot surfaces. They
concluded that the microtopography had a strong effect on
observed flow directions, producing small ponds along the
paths of flow and altering the flow depths and velocity fields.
Descroix et al. (2007) observed that catchments and small
plot studies in arid regions usually show a so-called “hortonian” trend, with characteristic absence of base flow. This
was the case in semi-arid northern Mexico for catchments
as large as tens of thousands of km2 , and for approximately 500 km2 in the Western Sierra Madre. Latron and
Gallart (2007) working at the Pyrenees determined that there
is a strong relationship between the base flow and the extension of saturated areas at the basin scale. In Australia’s
semi-arid rangelands, patches of bare soils were determined
to be the main run-off controlling factor (Cammeraat, 2002;
Bartley et al., 2006).
Thompson et al. (2011) observed that the lateral redistribution of ponded water generated during intense rainstorms
plays an important role in the hydrological, biogeochemical
and ecological functioning of patchy arid ecosystems. Lateral
redistribution of surface water in patchy arid ecosystems has
been hypothesized to contribute to the maintenance of vegetation patches through the provision of a water subsidy from
bare sites to vegetated sites (Bromley et al., 1997). A strong
control on field-scale infiltration is exerted by the horizontal spatial variability of infiltration properties (Lipsius and
Mooney, 2006; van Schaik, 2009). Such infiltration-overland
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
flow processes occur during hortonian run-off events on sloping ground. Surface flow redistribution may also occur on flat
ground if the presence of vegetation patches creates contrasts
in infiltration rate between dry soil and water saturated areas.
Changes in the pattern of surface water re-distribution occur during early stages of desertification (Ares et al., 2003).
Several studies indicate that the horizontal movements of
the naturally scarce rainfall water on the surface soil in arid
regimes contribute to define the spatial pattern of woody and
herbaceous vegetation forms as well as the extent of bare soil
patches (Aguiar and Sala, 1999; Ares et al., 2003; Borgogno
et al., 2009; Dunkerley, 2002).
Water infiltration in the soil has been successfully modelled through various techniques. Some existing models apply numerical solutions to the Richards equation (Radcliffe
and Simunek, 2010; Weill et al., 2011), while others use
various modifications to the Green-Ampt (Green and Ampt,
1911) model (Gowdish and Muñoz Cárpena, 2009; Mengistu
et al., 2012; Schröder, 2000).
Experiments and models on overland flow have extensively used so-called kinematic wave reduced solutions to the
Saint-Venant (S-V) equations (Mügler et al., 2011; Thompson et al., 2011). The numerical solutions of these reductions
require the estimation of frictional effects acting on overland
flow. Also, in order to construct continuity equations, the average depth of the overland flow must be known as well as
its propagation velocity. Although the S-V equations have
consistently proved capable of accurately simulating hydrographs at plot scale, most of the assumptions underlying the
estimation of frictional forces and flow depth do not hold
when applied to overland flows in field conditions (Smith et
al., 2007). Moreover, the choice of roughness models to be
used in the S-V equations is most often done with the purpose
of increasing the hydrograph quality, while the actual travel
time of water is ignored. In extended hydrological practice,
frictional factors are usually taken from published tables or
assumed spatially constant (Esteves et al., 2000).
Plot experimentation has long been relevant in developing
physically based models of water flow (Köhne et al., 2009).
The term usually refers to laboratory (Antoine et al., 2011;
Dunkerley, 2001, 2002; Legout et al., 2012) or field (Esteves
et al., 2000; Mengitsu et al., 2012) studies involving areas in
the scale of some few square meters, where water inflow conditions can be manipulated with varying success. Plot studies
on overland flows sometimes use natural rainfall falling on
the plot as water input (Esteves et al., 2000) or a controlled
water inflow either through rain simulation over the whole
plot surface (Abrahams et al., 1990; Biemelt et al., 2005;
Mügler et al., 2011), or through drippers, perforated pipes,
etc. at the top of the plots (Dunkerley, 2001, 2003; Hessel et
al., 2003). In these latter cases, a reduced area within the plot
receives the water input, while overland flow is observed at
the rest of the area. This is considered adequate since during storm events, surface routing, stem flows, etc. may result in water inflows relatively un-related to the instantaneous
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M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
rainfall input as a consequence of the position of the plot area
in the drainage network. Abrahams et al. (1990) used trickles to supply 140 000 mm3 s−1 to the top of 10 m2 plots in
studies of flow resistance in semi-arid environments, while
Dunkerley (2003) choose perforated pipes to deliver 1 × 103
to 9 × 103 mm3 s−1 to laboratory plots of 1.4 m2 .
Plot studies usually require some disturbance of naturally
occurring conditions, like constructing flumes (Esteves et al.,
2000; Giménez et al., 2004), modifying the soil surface to obtain desired flow channels (Mügler et al., 2011) or simulating
the soil surface with technical artifacts (Dunkerley, 2003).
Rainfall-run-off plot experiments where a device is used to
generate rainfall events mimicking natural conditions may
also require measuring the water flow at an outlet in order
to compute water mass balances (Grierson and Oades, 1977;
Cerdá et al., 1997). These experimental setups introduce artifacts affecting to some degree the characteristics of the overland flows as compared to those under field conditions.
Plot experiments are often used to obtain estimates of depression storage (DS) (Antoine et al., 2011) in studies of
overland flow, in the context of interpreting DS retention
effect on hydrograph records (Govers et al., 2000; Hansen,
2000; Darboux et al., 2001). The underlying concept is that
DS areas behave as a temporary passive storage of overland
flow resulting in a delay in the hydrograph signals. This in
turn prompts interest in its direct measurement at the plot
scale through geometrical analysis of elevation models (Planchon and Darboux, 2002) or from surface roughness measurements (Antoine et al., 2011).
Comparisons among results obtained in field studies on
overland flows at various semi-arid/arid environments might
benefit from biogeography analysis of the corresponding experimental sites. Regional similarities as estimated through
comparative biogeography (Parenti and Ebach, 2009) result
from analyzing spatial and functional patterns of biodiversity, species distribution, and geological history.
This study is part of a larger project at the National Patagonic Centre (Chubut, Argentina) to develop tools for the
eco-hydrological analysis of the desertification processes. It
builds on previous results obtained by Ares et al. (2003)
indicating that early desertification processes involve modifications of the overland flow patterns and its distribution
among the various vegetation life forms in the Patagonian
Monte (Argentina). Here, an experimental protocol is presented of the field plot experiments and coupled simulation
model to estimate infiltration and overland flow parameters
in the Monte environment. The protocol involves parameters
that can be quantitatively estimated with an adequate degree
of precision (overland flow velocity, infiltration depth, soil
water content, depression storage area) as well as others that
can indirectly be estimated through modelling results (surface frictional effect, average overland flow depth, ReynoldsFroude numbers). Specifically, this study addresses: (1) the
effect of plot microtopography on infiltration-overland flows,
and (2) the estimation of overland flow parameters (velocity,
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3295
depth, friction) needed to characterize water movement at the
soil surface. A biogeography analysis of the similarity of the
experimental site in this study with other areas of the world
is also included to ease eventual comparisons of the results
presented here with those obtained in similar studies.
2
2.1
Site and field experiments
Biogeography of the experimental site
The Monte desert is a South American subtropical to warm
temperate desert and semi-desert located in western Argentina from 24◦ 150 S to 44◦ 200 S. The study here presented
was performed at a representative site of the biome in the
area of the Patagonian Monte, a temperate region with a
Mediterranean-like rainfall regime produced by the Westerlies from the Pacific affected by the rain shadow effect
from the Andes (Abraham et al., 2009). Past precipitation
records, observed (Haylock et al., 2006) and predicted precipitation anomalies expected under various scenarios of climate change (Carrera et al., 2007), indicate that precipitation
events may occur at both high (> 20 mm day−1 ) as well as
low (< 3 mm day−1 ) depths. This pattern corresponds to alternative atmospheric mechanisms of rain generation characteristic of the tropical regime prevailing at the northern part
of the territory or prevailing winter-rain of the temperate latitudes (Prohaska, 1976). Both types are observable at times
along most of the area occupied by the biome. There is a
remarkable convergence between the desert areas of North
and South America (Monte, Chihuahuan-Sonoran deserts)
consisting in the same climate subtypes, the same dominant
vegetation and the same combination of biological forms
(Morello, 1984 as quoted by Abraham et al., loc. cit.). Similar conditions are extensively found in arid and semi-arid
climates worldwide (Mares et al., 1985).
This study was carried out at the wildlife refuge “La Esperanza”, (southern portion of the Monte desert) which occupies
an area of about 42 000 km2 in southeastern Argentina (León
et al., 1998; Soriano, 1950). The mean annual temperature
is 13.4 ◦ C and the mean annual precipitation is 235.9 mm
(1982–2001). The characteristics of the site as representative
of the Monte desert are based on the analysis of the dominant vegetation life forms. The local vegetation covers about
40 % and 60 % of the soil in a random patchy structure with
three vegetation layers: the upper layer (1–2 m height) dominated by tall shrubs (Larrea divaricata, Schinus johnstonii
Barkley, Chuquiraga erinacea Don., Atriplex lampa Gill. ex
Moq., and Lycium chilense Miers ex Bert.), the intermediate layer (0.5–1.2 m height) also composed by dwarf shrubs
(Nassauvia fuegiana (Speg.) Cabrera, Junellia seriphioides
(Gillies and Hook) Mold., and Acantholippia seriphioides
(A. Gray) Mold.), and the low layer (0.1–0.5 m height) dominated by perennial grasses (Nassella tenuis (Phil.) Barkworth, Pappostipa speciosa (Trin. and Rupr.) Romasch, and
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
3296
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
Poa ligularis (Nees ex Steud)) (Ares et al., 1990; Carrera et
al., 2008). Soils are a complex of Typic Petrocalcids–Typic
Haplocalcids with a fractured calcium carbonate layer from
0.45 to 1 m below the soil surface (del Valle, 1998). Upper
soil texture types (USDA) are sandy or loamy sand.
2.2
Field experiments
Ten field plot experiments in undisturbed bare soil patches
(800 × 800 mm) along a 540 m, down-sloping (−7.2 %) tranS1
sect from S: −42.17046, W: −64.96343 to S: −42.21366, W:
−64.99225 were conducted during the dry season on days
S2
with air temperatures in the range of 20–32 ◦ C. The spatial arrangement of plots was aimed to explore an altitudinal
range of variation of soil texture. Water inflow to plots was
Control
applied at mid/low-slope length locations of inter-mound soil
S3
areas through a portable, wind protected, single-nozzle system mounted at 30 cm above soil level on a wooden frame,
Fig. 1. Left panel: overhead view of a field plot in this study at the
and calibrated with a pressure gauge to supply water inend of the water inflow period with TDR probe position marks and
3
−1
flow rates in the range 225–4500 mm s to a small area
spikes with control marks used in the CRS-GSM procedure. Right
(4.7 ± 5.2 %) of each plot that was further neglected for espanel: soil cores along the main axis of the overland flow area are
timations of overland flow velocities. This created two Fig.
plot1. (left) already
Overheadextracted.
view of a field
plotoccurred
in this study
at the
end of theS1
water
inflow period with
Flow
in the
direction
to S3.
sub-regions: one directly receiving the water inflow andTDR
an-probe position marks and spikes with control marks used in the CRS-GSM procedure. (Right).
other receiving the overland flow resulting from the excess
Soil cores along the main axis of the overland flow area are already extracted. Flow occurred in the
of water input to the former. The water inflow range was
(ISO 11272, 1998) at a nearby location. Maps of soil
direction S1 method
to S3.
aimed to simulate flow accumulation values at the spatial
moisture in the wetted area at the end of the water inflow
scales of this study as estimated with a flow routing algoperiod were based on calibrated TDR estimates. Map valrithm (Tarboton and Ames, 2001). The frame supported a
ues were obtained by interpolation of 4–6 closest TDR esKodak EasyShare Z712 IS 7.1 MP camera (© Eastman Kotimates, based on a search radius algorithm (Idrisi v. 14.02,
dak Company, Rochester, New York) with video mode, at
Clark Labs, Worcester).
near zenith position over the centre of the plot and about
The texture of the extracted soil core samples was mea1 m above ground level to obtain images of the whole plot
sured with Lamotte’s 1067 texture kit (LaMotte Co., Chesterarea. Video records of the expanding overland wetted artown) calibrated with replicate estimates obtained at two
eas were obtained during experiments of varying time length
reference laboratories (National Patagonic Centre, National
(72–1128 s) until the wet front reached some of the borders
University of the South, Argentina) with the Robinson’s proof the camera image in any direction. This implied a zerotocol (Gee and Bauder, 1986). Parameters corresponding to
discharge condition (all overland flow was infiltrated within
residual volumetric moisture (θr ), saturated moisture conthe observed plot areas at the end of the experiments).
tent (θs ), saturated hydraulic conductivity (Ksat ) tortuosity1
Soil moisture was evaluated immediately after the waconnectivity (L), and shape of the soil moisture-water head
ter inflow ceased with a TDR (Time-Domain Reflect meter,
function (log10 α, log10 n) (Van Genuchten, 1980) corresponding to the obtained soil samples were estimated based
TRIME® -FM, Ettlingen) pin (50 mm) probe inserted at a
on textural data through an ANN (Artificial Neural Net) peproper angle in order to sample the top 30 mm of the soil at
dotransfer algorithm (Rosetta v. 1.2, US Salinity Laboratory,
equidistant (30–35 mm) points of a grid covering the whole
Riverside) developed by Schaap and Leij (1998).
overland flow area and neighbouring dry points. TDR estiA methodology (Rossi and Ares, 2012) combining Closemates of soil moisture were calibrated with gravimetric estiRange Stereophotogrammetry (CRS) and Geo-Statistical
mates (y = 1.166 x + 0.05; R 2 = 0.92, n = 101; x: gravimetric
Modelling (GSM) was applied to obtain Digital Elevaθ estimate) obtained by extracting 2–5 soil cores (Ø: 40 mm)
tion Models (DEM) (resolution 8.23 ± 0.24 mm, P < 0.05,
along the main axis of the overland flow plumes, at the cenn = 10). The coordinates of 9 control points and a minimum
tre of the directly wetted area and equidistant positions up
of 64 targets obtained through CRS were loaded to an applito the wetted border and control at nearby dry soil (Fig. 1).
cation (I-Witness v. 1.4, DCS Inc., Bellevue, WA, USA) for
Soil cores were extended to depths 0–30, 30–90 and 90–
orthorectification and further processed with a kriging algo180 mm, brought to the laboratory in sealed containers and
rithm (Surfer v. 7, Golden Software Inc., Colorado) to obtain
wet-dry (105 ◦ C) weighed for moisture content. Gravimetric
plot DEMs and DEM-based flow vector fields. Digital videomoisture was expressed in volumetric terms through correcimages of the overland flowing water plume were selected
tion with soil bulk density measured through the excavation
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
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M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
at regularly spaced time intervals (6–240 s). The spacing of
time intervals within this range was selected according to
the duration of the experiments. Time intervals were constant (Ti = 6 s) for those experiments of short duration with
relatively higher water input rates (Plots 1 to 4). In longer
experiments with low water input rates (Plots 5 to 10), time
intervals (s) were selected according to Ti = (e(0.265×ts) ) × 6,
where ts is the cardinal number of the interval. This resulted
in 10–18 images at short intervals during the early stages
of fast overland flow and gradually longer intervals during
later stages of slow overland flow. Images were then exported
to an image processing application (Idrisi v. 14.02, Clark
Labs, Worcester), ortho-rectified (RMSE: 7.59 ± 1.3 mm,
P < 0.05, n = 10) and overlaid to their corresponding plot
DEM and map of flow vector fields at the same resolution
of the DEM. Flow vectors were estimated from the DEM. At
any map node, flows were in the direction of the steepest descent and the magnitude of the arrow depended on the steepness of the descent. The terrain height change corresponding
to the overland flow advance at each time interval was evaluated by averaging the altitude differences between all pixels
along the borders of successive images.
Depression storage (DS) (Antoine et al., 2011) areas were
identified at each sampling interval (tn+1 , tn ) by measuring
the area A(t)n+1 − A(t)n advanced by the overland plumes
during the n-th interval, discriminating between: (1) area
advanced down slope, and (2) area advanced in a counterslope direction (CSA, Counter-Slope-Advance). CSA estimates were then weighed to correct for great advances at flow
start and small advances at flow end:
w(t) =
A(t)(n+1) − A(t)(n)
,
A(t)(n+1)
(1)
and DS was expressed as the accumulated CSA areas as a
percent of A(t)n+1 (also see Fig. 2):
t=n
P
CSA(t)(n+1) × w(t) × 100
t=1
.
(2)
DS(t)% =
A(t)(n+1)
3
Model
The changes observed at the overland flow areas and subsurface soil water content at the plots were modelled with
a physically based continuity model consisting of a set of
non-linear ordinary differential and continuity equations with
time variable parameters representing the changes in storages of overland water (Eq. 3) and at the upper vadose zone
(Eq. 4):
dQo
= W − IN(t) − O(t)
dt
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(3)
dQv
= IN(t)
dt
CW = Qo + Qv .
3297
(4)
(5)
Qo : Water stored at the overland plume (mm3 ).
Qv : Water stored at the upper vadose zone (mm3 ).
W : Water inflow (mm3 s−1 ).
IN(t): Total infiltration flow (mm3 s−1 ).
CW: Cumulative water inflow (mm3 ).
O(t): overland flow (mm3 s−1 ).
Note that evaporation was disregarded due to the short duration of the field experiments. While W is time constant
for each single plot experiment, INt − Ot can be expected
to change with time depending on the effects of soil microrelief and the physical properties of the surface soil. Further,
the overland flow plume includes DS areas where water accumulates during the water inflow period, and other parts where
the water inflow is not enough to maintain free water at the
soil surface. Accordingly, IN(t) may be expected to result
from the composition of flows under both saturated and unsaturated conditions. Saturated conditions occur at DS areas,
while both saturated and/or unsaturated infiltration flows can
occur at other areas depending on their water content:
IN(t) = INsat (t) + INunsat (t).
(6)
INsat (t): transient, saturated infiltration flow at DS areas
(mm3 s−1 ).
INunsat (t): transient, saturated and/or non-saturated infiltration flow at non-DS areas (mm3 s−1 ).
The INsat flow was modelled through a Darcy’s law concept, where infiltration was assumed to occur under saturated
conditions depending on the gradient of water head between
the soil surface and a point at the infiltrating wetting front
(see Appendix A):
θs − θ (t)
(7)
+ 1 × ADS
INsat = Ksat × ψf ×
F
F = zf (t) × (θs − θ (t)) .
(8)
Ksat : saturated hydraulic conductivity (mm s−1 ).
ψf (θ ): suction at the wetting front (mm).
θs , θ (t): saturation and instantaneous volumetric water content at the wetting front respectively (dimensionless).
F : accumulated infiltration (mm).
ADS : DS area (mm2 ).
zf (t): instantaneous water infiltration depth (mm).
In areas of the overland plume where no DS occurs, water
infiltration was assumed to occur under unsaturated conditions (see Appendix A). Replacing in Eqs. (7) and (8) through
corresponding terms:
θ (t) − θi
INunsat (t) = Kh (θ (t)) × ψf (θ (t)) ×
+1
F
× (A(t) − ADS ) .
(9)
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
3298
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
a
A
B
C
D
x1
Soil profile
x2
Plume front (tn+1)
Plume front (tn )
b
tn: 6 s; tn+1 : 16 s
tn: 340 s; tn+1 : 450 s
CSA areas
Fig. 2. Estimation of local CSA (Counter-Slope-Advance) overland plume areas in this study. (a) An example of a soil profile at x1 − x2
with micro-depressions (A–D). An overland plume advances down-slope from left to right up to depression C, over totally ponded A–C and
partially ponded B. Plume fronts circumscribe plume areas A(t)(n) and A(t)(n + 1) (see Eqs. 1–2). Part (red areas) of the plume advances
occur up-slope while the plumes fill depressions and finally overflow the depression boundaries. (b) Scene examples (lower insets) of plume
advances at Plot #10 at two sampling intervals. Left panel: tn : 6 s, tn+1 :16 s; right panel: tn : 340 s, tn+1 : 450 s after water inflow start, overlaid
on the plot DEM (contour interval: 1 mm) with DEM-based flow arrows.
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
1
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M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
3299
Table 1. Calibration parameters and variables of soil surface and upper vadose and convergence criteria used in tuning a model of the field
plot experiments. ANN CI: Confidence interval of the ANN estimation process; r: correlation coefficient, linear regression model-data values
(xmodel = a + b × xdata ; H0 : a = 0, b = 1) over all plot experiments. (A(t)): convergence evaluated at 10–15 times during the water inflow
period (∗∗ : statistical significance at P < 0.05).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Parameter
Convergence criteria
Compartment
Sand (%)
Silt (%)
Clay (%)
θsat
θr
θantecedent
Water inflow W (mm3 s−1 )
Water inflow period (s)
Ks (mm s−1 )
Wet Area (A(t)) (mm2 )
Total Wet Area (A∗ ) (mm2 )
Average run-off velocity (mm s−1 )
Average S (mm)
Average DS area (%)
θend
End zf (mm)
Water mass balance error (mm3 )
Data value
Data value
Data value
Data value
Data value
Data value
Data value
Data value
ANN CI − r ∗∗
EC ≥ 0.99∗
r ∗∗
r ∗∗
r ∗∗
r ∗∗
r ∗∗
r ∗∗
e < 1 × 10−6 mm3
Soil
Soil
Soil
Soil
Soil
Soil
Surf. soil
Surf. soil
Soil
Surf. soil
Surf. soil
Surf. soil
Surf. soil
Surf. soil
Soil
Soil
Soil
∗ Nash and Sutfliffe (1970).
Kh (θ (t)): variable hydraulic conductivity (mm s−1 ).
θi : Antecedent water content of the soil.
A(t): Wet area of overland plume at time t (mm2 ).
Kh (θ (t)) and ψf (θ (t)) were estimated through the solution
(van Genuchten, 1980) of Mualem’s (Mualem, 1976) formulation to predict the relative hydraulic conductivity from
knowledge of the soil-water retention curve.
The instantaneous overland water volume was estimated
as
Qo = A(t) × d(t).
(10)
d(t): average depth of the overland flowing water volume at
time t (mm).
Flowing in the x-y space, with varying velocity depending
on the local altitude gradient along its border, such that d(t)
is inversely related to the slope of the underlying soil surface.
This relation would follow Darcy’s general form of frictional
law (Dingman, 2007; Mügler et al., 2011):
d(t) =
W
C
2
/S(t, t + dt).
(11)
C: Proportionality constant.
S(t, t + dt): Average terrain height drop around the overland
plume during the interval t, t + dt (mm).
Where the velocity term is replaced in this case with the
water inflow rate W , and S(t, t − dt) was obtained from successive video images of the overland flow overlaid on the plot
DEMs. The term C was found through inverse modelling of
www.hydrol-earth-syst-sci.net/16/3293/2012/
the continuity Eqs. (3)–(5), solved through numerical integration with a fourth-order Runge-Kutta approximation, at
solution time intervals 0.06 ≤ 1t ≤ 0.3 s, and an accepted
mass balance error threshold e ≤ 1 × 10−6 mm3 .
Modelling parameters and variables: calibration and
validation
Table 1 summarizes the parameters and variables used to calibrate the model of the field plot experiments. Model calibration was achieved through trial-error on parameter C
and simultaneous calibration on parameters 9–16 (Table 1).
In order to restrict the possibility of compensatory artifacts
during the calibration process, the quality of the calibration
procedure was evaluated through simultaneous convergence
of all measured values describing the experimental setting,
the morphology of the plot surface soil and the texturalhydrological properties of the upper vadose zone. The criteria in the case of parameters 1–8 was strict convergence
to measured data values. Convergence of parameter 9 (Ks )
was pursued within the confidence interval of the ANN estimation process as reported in Shaap and Leij (1998). Variable 10 (A(t)) was required to converge to time-serial data
as estimated through a Nash-Sutcliffe’s efficiency coefficient
(EC ≥ 0.99) (Nash and Sutcliffe, 1970). Values of 11–16
were required to converge to:
6i=1,n (xi − xdata )2 = min
(12)
where xi is the model estimate and xdata is the corresponding experimental-measured value. 11–16 were further tested
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
for convergence to data at the inter-plot scale such that their
correlation with measured values would be significant at
P < 0.01 over the set of 10 plots studied. Variables 12–14 are
average values of the corresponding variable over the simulation time.
Several procedures were used for model validation. Unit
consistency and ranges of Ks , Kh (θ(t)), and ψf (θ(t)) were
independently checked through comparison with estimates
obtained with CHEMFLO-2000 (Nofziger and Wu, 2003), an
application that solves Richards equations in one-dimension
to simulate transient water (and chemical) transport in soils.
In order to detect eventual spurious correlation values (Table 2, column “r”) resulting from outlier data points, confidence intervals (P < 0.05) of the correlation coefficient r of
measured-modelled values 9–16 were built by bootstrapping
randomly selected paired 5-plot sets. zf and θend values observed in the field were additionally tested for consistency
with CHEMFLO-2000 estimates.
Additionally, the following variables were defined based
on model outputs:
ς ∗ = 6t=1,n (O(t)/W (t) /n .
(13)
ς ∗ : mean run-off coefficient
where ς ∗ is a mean (dimensionless) run-off estimate, of
ς = O(t)/W (t), including transient depression storage.
d ∗ = 6t=1,n d(t) /n .
(14)
(15)
v ∗ : mean overland flow velocity (mm s−1 ).
Several parameters of the experimental plots which are
usually estimated in overland flow studies (Abrahams et al.,
1990; Parsons et al., 1994; Dunkerley, 2001) were also computed to ease comparisons of conditions in this study with
reported data. As long as basic assumptions underlying their
rationale are granted, the Froude number (F ) relates the velocity of the overland laminar flow to the expected velocity
of a gravitational wave, or the ratio of the laminar flow inertia to gravitational forces. Analogously, the dimensionless
Reynolds number (Re) gives a measure of the ratio of inertial forces to viscous forces for given flow conditions. High
Reynolds numbers characterize turbulent flow.
4
Results
Table 2 summarizes results obtained from the plot experiments and the calibration of their models. The upper vadose zone (zf ≤ 55 mm) of all plots showed various combinations of sand, silt and clay fractions within the boundaries
of Sandy-Loam and Loamy-Sand USDA textural classes (Parameters 1–3) as well as their basic hydraulic properties (parameters 4–5, 9). The values of parameter 6 corresponded to
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
Plot 6
Plot 8
Plot 10
0.05
0.10
0.15
0.20
0.25
0.30
0.35
100 mm
Fig. 3. Upper soil moisture (θend , 0–30 mm) maps of the overland
plumes based on TDR probing (black dots) at the end of the water
inflow
periods at four plots in this study. Yellow circles indicate the
Fig. 3. Upper soil moisture (θend , 0-30mm ) maps of the overland plumes based on TDR
water
inflow
areas. Maps overlay rectified plot photos and correprobing (red dots) at the end of the water inflow periods at four plots in this study.
sponding level (mm) contour lines.
Yellow circles indicate the water inflow areas. Maps overlay rectified plot photos and
corresponding level (mm) contour lines.
d ∗:
mean d(t) (mm)
0.5 v ∗ = A∗
tend .
Plot 5
0.00
100 mm
3300
4
very dry conditions of the upper soil due to the fact that all the
plot experiments were performed during the dry season of the
local climate regime. The range of water input flows (parameter 7) produced groups of relatively fast and slow overland
flow and water infiltration conditions. Calibration values of
Ksat and parameters 11–16 were significantly correlated with
data values. H0 : a = 0, b = 1 was rejected in the case of parameter 16 (zf,model = −8.41 + 0.955 × zf,data , P = 1.42E-06).
This is to be expected due to the fact that zf,data were estimated from soil cores along the main overland flow axes,
while zf,model expresses the average infiltration depth corresponding to the whole wet area. The modeled time series of
overland flow areas A(t) (variable 10) were in all cases significantly correlated with the observed areas as indicated by
the Nash-Sutcliffe’s EC.
Figure 3 shows examples of maps of the distribution of
upper vadose zone (0–30 mm) moisture (θend,0-30mm ) at four
plots in this study as obtained with the TDR probe at the
end of the water inflow period. Depending on the position of
the water inflow and the local microtopography, some areas
contain moisture at near saturation levels while various levels
of unsaturated conditions prevailed at other areas.
Figure 4 shows comparisons of zf and θend values as obtained from the CHEMFLO-2000 simulation with estimates
from the model in Sect. 3; photographs of soil cores at the
water inflow areas are also shown for comparison. Figure 5
www.hydrol-earth-syst-sci.net/16/3293/2012/
0.06
4500
72
8.2E-03
1.1E-02
0.996b
1.5E+05
1.6E+05
5.55
5.56
14
23
8.E-09
Clay (%)
θsat
θr
θantecedent
Water inflow W (mm3 s−1 )
Water inflow period (s)
Ks (mm s−1 )
Wet area (A(t)) (mm2 )
Total wet area (A∗ ) (mm2 )
Average run-off velocity (mm s−1 )
Average S (mm)
Average DS area (%)
θend
End zf (mm)
Water mass balance error (mm3 )
3
4
5
6
7
8
9
10
11
12
13
www.hydrol-earth-syst-sci.net/16/3293/2012/
14
15
16
17
−1.E-09
12
21
0.21
0.21
2.7
1.7
1.8
1.6
1.96
1.98
3.7E+04
3.6E+04
0.994
1.1E-02
9.7E-03
96
4500
0.05
0.05
0.38
9.2
10.3
80.8
P2
All model estimates in bold italics.
a Confidence interval (∗∗ ) of the mean of 5 random samples out of 10 values.
b Nash-Sutcliffe’s efficiency coefficient (see also Fig. 5).
0.19
0.19
3.67
4.72
0.3
0.2
0.04
0.38
7.3
12.0
Silt (%)
2
80.7
Sand (%)
P1
1
Parameter, variable
Table 2. Experimental results and model parameter values.
2.E-10
13.5
24
0.19
0.19
2.9
2.76
4.5
4.6
4.77
4.73
5.2E+04
5.1E+04
0.996
8.2E-03
5.7E-03
48
4500
0.06
0.05
0.39
12.0
13.8
74.2
P3
2.E-10
12
18
0.20
0.20
0.74
0.28
1.8
1.5
5.24
5.25
1.4E+05
1.4E+05
0.997
5.8E-03
4.7E-03
72
4500
0.11
0.05
0.38
14.4
14.4
71.2
P4
−1.E-07
36
47
0.18
0.18
7.36
5.65
1.2
1.5
0.20
0.21
5.3E+04
5.5E+04
0.990
5.3E-03
6.2E-03
1128
308
0.05
0.04
0.38
16.7
14.9
68.4
P5
6.E-10
43
53
0.20
0.20
14.15
13.2
2.7
3.4
0.23
0.22
5.4E+04
5.3E+04
0.990
5.3E-03
8.2E-03
1026
442
0.04
0.04
0.39
6.5
17.3
76.2
P6
Plots
6.E-10
24
28
0.13
0.13
10.61
11.99
0.5
0.7
0.47
0.47
1.1E+05
1.1E+05
0.994
1.2E-03
4.2E-03
714
450
0.05
0.05
0.38
14.0
15.6
70.4
P7
2.E-10
37
42
0.13
0.12
1.28
1.13
1.0
1.0
0.41
0.42
7.4E+04
7.5E+04
0.995
2.9E-03
3.6E-03
660
408
0.05
0.05
0.38
14.4
20.1
65.5
P8
−3.E-10
34
45
0.19
0.20
21.31
19.8
2.1
1.8
0.34
0.34
7.3E+04
7.3E+04
0.999
4.5E-03
4.4E-03
792
500
0.06
0.05
0.38
16.0
10.4
73.6
P9
−3.E-10
44
55
0.17
0.17
16.2
16.8
0.3
0.3
0.21
0.21
3.2E+04
3.2E+04
0.998
4.6E-03
5.9E-03
852
225
0.06
0.05
0.38
12.8
10.4
76.8
P10
0.930
0.810
0.862
0.889
0.999
0.999
0.775
r
1.6E-02
2.2E-02
2.2E-02
2.5E-02
1.7E-04
2.5E-04
9.0E-02
CIa
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
3301
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
3302
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
Table 3. Froude (F ), Reynolds (Re) numbers and C, d ∗ parameter values and slopes (s, %) of the field plot experiments.
1
2
3
4
5
Fa
Reb
C
d∗
s
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
0.096
8.39
9.50E+04
0.34
1.1
0.006
101.77
4.80E+03
11.40
14.0
0.033
45.76
7.60E+03
2.16
2.9
0.051
16.22
1.50E+04
1.09
7.2
0.005
0.19
3.50E+03
0.21
7.8
0.001
3.71
8.60E+02
3.70
1.7
0.012
0.33
7.00E+03
0.16
2.2
0.008
0.84
4.6E+03
0.28
5.5
0.005
0.68
3.20E+03
0.45
11.0
0.005
0.18
5.0E+03
0.19
3.0
a F = v ∗ /(g × d ∗ )0.5 ; g = 9806.65 mm s−12
b Re = 4 × v ∗ × d ∗ /v ; v = 0.9 mm2 s−1
Plot 3
160
60
80
40
40
20
0
-60
0.4
0.6
(v/v)
40
60
80
Time (s)
160
20
Plot 4
3
Data
Model
Data
Model
120
15
80
10
40
5
2
0
20
3
0.2
Total Area (mm x 10 )
-40
-80
-120
0
0Plot 8
0.2
0.4
0
0
0.6
0
40
60
80
Time (s)
120
80
Plot 7
Data
Model
Data
Model
3
Total Area (mm x 10 )
20
60
60
40
30
20
-40
-60
0
0.2
0.4
2
3
90
2
-20
DS (mm x 10 )
Depth (z
(cm)
Depth
f , mm)
0Plot 6
Depth (cm)
0
0
2
-40
DS (mm x 10 )
-20
2
2
3
120
DS (mm x 10 )
3
Total Area (mm x 10 )
Depth (zf , mm)
0
80
Plot 1
0.6
0
θ end (v/v)
(v/v)
0
0
200
400
600
800
Time (s)
Fig. 4. Comparison of zf (photo insets) and θend field soil core data
(circle-lines) used as an input to the model in this study and estiData
Model
Data
Model
mates through CHEMFLO-2000 (lines). Soil core photos obtained
immediately after ceasing water inflow are also shown.
5. The progression
overland
A(t)
andthe
DSwater
areas
durFig. 5.Fig.
The progression
of overlandof
flow
A(t) and flow
DS areas
during
inflow
ing the water inflow periods in three field plots as estimated from
periods in three field plots as estimated from rectified video imagery and the model
rectified video imagery and the model used in this study.
used in this study.
omparison of zf (photo insets) and θend field soil core data (circle-lines) used as
6
model in this study and estimates through CHEMFLO-2000 (lines). Soil core
btained immediately after ceasing water inflow are also shown.
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
www.hydrol-earth-syst-sci.net/16/3293/2012/
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
Plot 1
Plot 2
9.0E+04
3303
y = 2509.7e
38.22x
2
R = 0.88
C
ς
6.0E+04
3.0E+04
Plot 3
Plot 4
0.0E+00
ς
0.00
0.03
0.06
0.09
0.12
F
Fig. 7. Inter-plot statistical relations between parameters C–F .
Fig. 7. Inter-plot statistical relations between parameters C-F .
Plot 6
5
ς
Plot 5
Plot 8
Plot 9
Plot 10
ς
ς
Plot 7
DS (%)
DS (%)
Fig. 6. Intra-plot time-serial relations between the estimated DS and
Fig.
Intra-plot
relations between the estimated DS and the runoff (ς)
the6.runoff
(ζ time-serial
) coefficient.
coefficient.
shows A(t) values and point and average estimates of DS
areas of several plots as measured and estimated with the
model of Eqs. (3)–(5).
No significant correlations were found between the extent
of DS areas and other variables at the inter-plot scale. At
intra-plot scale (time-serial values corresponding to sampling
time intervals at each experimental plot) run-off (ς ) values
were variously related to DS (Fig. 6) depending on the water
inflow. At plots 1–4 (high inflow rate), decreasing relations
were observed. Run-off increased with DS estimates at most
plots under low water inflow.
Table 3 summarizes theoretical hydrodynamic overland
flow parameters of the plot experiments and Fig. 7 shows
the relation C–F .
www.hydrol-earth-syst-sci.net/16/3293/2012/
7
Discussion
In plot experiments where natural or simulated rain occurs
over the plot area the kinetic energy of the rainfall may
modify the overland flow momentum and velocity. Measured
ranges of rainfall kinetic energy all over the world under various methods indicate a range of 12–22 J m−2 mm−1 for a
storm of 10 mm h−1 (Rosewell, 1986), which is a common
event in semi-desert areas under tropical regime. Aside from
potential effects on soil microtopography (erosion) these energy inputs can reasonably be expected to contribute to the
overland flow momentum balance.
Flume plot experiments (Esteves et al., 2000; Dunkerley,
2004) may introduce various kinds of artifacts. To avoid wall
effects, the soil relief must be manipulated in order to deliver
the overland flow to the central part of the flume. In laboratory flume experiments, the natural soil must be transported
and necessary modifications in soil structure must follow.
Overland flow studies using technical materials to simulate
the soil surface might not reproduce field conditions.
Experiments on overland flow involving the measurement
of run-off through an outlet (a need in computing water mass
balances and runoff coefficients) may require modifications
of the soil microtopography to deliver run-off to the outlet.
Interflow measurement (Wang et al., 2011) might require sophisticated outlet configurations.
Some of the above mentioned potential limitations of plot
studies on overland flow were addressed through the experimental setup in this study. Estimates of overland flow depth,
velocity and friction were obtained without manipulation
of the microtopography of field plots; overland-infiltration
flows were considered simultaneously and the effect of depression storage areas was estimated. Inertial forces acting
on the overland flows were small as estimated through F
numbers (Table 3). Flows were predominantly laminar (see
Re numbers, Table 3).
The consideration of the soil as a heterogeneous system at
physical non-equilibrium (PNE) has been applied to a number of hydrological models (see Köhne et al., 2009 for an extensive review of various forms of published PNE models).
In most cases, the emphasis has been focused on the effects
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
8
3304
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
of sub-surface soil heterogeneity on infiltration flows. In this
study, attention is given to surface soil heterogeneity in the
x-y plane and it is hypothesized that infiltration must occur
under saturated conditions at DS areas, while both saturatedunsaturated infiltration could occur at non-DS areas. This
interpretation is consistent with observations on composite
overland flow by Abrahams et al. (1990) on run-off plots in
arid southern Arizona (USA), where flow occurred as shallow sheets of water with threads of deeper, faster flow diverging and converging around surface protuberances, rocks, and
vegetation.
The results presented in Fig. 6 indicate that the effect of
DS areas on the overland flow (as estimated through the runoff coefficient) is more complex than expected from considering those as areas of passive transient water storage. The
effect of DS areas may result from various transient balances
of inflow, overland flow and infiltration. This view is supported by the results of the time serial relations DS-ς which
are predominantly increasing at plots with low rates of water inflow and decreasing at plots with high water inflow.
In explaining these trends, it should be considered that after the initiation of a water inflow exceeding the infiltration
rate (plots 1–4), DS areas become filled before the underlying top soil reaches saturation. This is reflected in shallow
end zf values (23.7 ± 3.9 mm, see Table 2, #16). The DS effect on overland flow approaches that of a passive storage
and results in decreasing DS-run-off relations (Fig. 6). In the
cases of plots receiving low inflows during longer periods
(Plots P5–P10), the water inflow is nearly balanced by the
saturated infiltration at DS areas. In these plots deeper zf values (45 ± 10.1 mm, see Table 2, #16) were observed. Once
the upper soil profile under DS areas becomes saturated, infiltration in DS areas diminishes reaching a low, steady rate
(Mao et al., 2008) and the run-off flow increases with increasing DS.
Equations (11) and (14) allow the estimation of the average overland flow depth d ∗ once the term C is estimated
through inverse modelling of the continuity Eqs. (3)–(5). The
term C is similar to the Chezy frictional constant, in that the
flow velocity (v) is replaced by the water inflow rate (W ) in
Eq. (11). However, C is indeed a friction descriptor as confirmed through its high correlation with the Froude number
(Table 3, Fig. 7).
Values d(t) − d ∗ (Table 3) obtained in this study are in a
similar scale as those reported by Esteves et al. (2000) and
instrumentally measured by Dunkerley (2001) in laboratory
conditions and Smith et al. (2011) in field conditions.
6
Conclusions
This study gives the following findings about the effects of
depression storage and infiltration on overland flow characteristics: (1) overland flow properties (velocity, depth, friction) as well as infiltration-overland flow mass balances are
Hydrol. Earth Syst. Sci., 16, 3293–3307, 2012
consistently modelled by considering variable infiltration
rates corresponding to depression storage and/or non-ponded
areas. (2) The effect of DS on run-off varies depending on the
local soil balance of water inflow and infiltration, the latter
modified by the local microtopography.
A protocol of experiments in undisturbed field conditions
and coupled time-distributed modelling to 1–2 above is described. A biogeography-based analysis of the experimental
site is given to ease comparisons with experiments on overland flows in other areas of the world.
Appendix A
Saturated-unsaturated infiltration
Consider a soil profile at an experimental plot surface
(Fig. A1) receiving a continuous water inflow (W ). A water
front at the soil surface limits a soil area where simultaneous
saturated infiltration occurs at ponded areas, and un-saturated
infiltration occurs in non-ponded sectors.
Saturated infiltration can be estimated from Darcy’s
equation:
q = Ksat
= Ksat
dh
h2 − h1
(ψf + zf ) − (d + 0)
= Ksat
= Ksat
dz
z2 − z1
zf − 0
ψf + zf − d
,
zf
(A1)
where
q = infiltration rate at saturated condition (mm s−1 ),
Ksat = saturated hydraulic conductivity (mm s−1 ),
ψf = suction at wetting front (mm),
d = the depth of overland flow (mm).
A cumulative depth of infiltration F (mm) is defined:
F = zf (θs − θi ) ,
(A2)
where
θi = initial volumetric moisture content (dimensionless) and
θs = saturated volumetric moisture content (dimensionless),
rearranging Eq. (A2) and substituting into Darcy’s equation:
ψf + θs −Fθi − d
dF
= Ksat
F
dt
θs − θi
F
θs − θi
= Ksat ψf +
−d
.
θs − θi
F
q =
(A3)
Assuming d is small relative to the other terms, the previous
equation simplifies to
dF
θs − θi
INsat =
= Ksat ψf
+1 ,
(A4)
dt
F
which is the Green and Ampt infiltration rate equation. When
the soil is not saturated, the infiltration rate can be calculated as in Eq. (A1) substituting into the Buckingham-Darcy
equation:
www.hydrol-earth-syst-sci.net/16/3293/2012/
5
simultaneous saturated infiltration occurs at ponded areas, and un-saturated infiltration
occurs in non-ponded sectors.
M. J. Rossi and J. O. Ares: Infiltration and overland flow at desert condition
3305
W
d
A
10
B
C
z
ψf
Overland flow front
z1
z2 (zf)
h1= d
h2= ψf + zf
Infiltration front
15
Fig. A1. Schematic representation
of parameters
involved inof
considering
depth zf of infiltration
a water inflow
Fig. I-1. Schematic
representation
parametersinfiltration
involvedup
in to
considering
up W on sloping soil with
partially ponded depressed areas (A–C) (also see main text, Fig. 2).
to depth zf of a water inflow W on sloping soil with partially ponded depressed areas (A-
C) (Also see main text, Figure 2).
Antoine, M., Chalon, C., Darboux, F., Javaux, M., and Bielders,
dh
h2 − h1
(ψf + zf ) − (d + 0)
C.: Estimating changes in effective values of surface detention,
q = Kh
= Kh
= Kh
dz
z2 − z1
zf − 0
depression storage and friction factor at the interril scale, using a
ψf + z20
and equation:
fast method to mold the soil surface microtopography,
Saturated infiltration can be estimated fromcheap
Darcy's
f −d
,
= Kh
(A5)
Catena,
91,
10–20, 2011.
zf
Ares, J. O., Beskow, M., Bertiller, M. B., Rostagno, C. M., Iris-
arri, M., Anchorena, J., Deffosé, G., and Merino, C.: Structural
where Kh (θ ) and ψf (θ) are the variable hydraulic conductiv(
ψ f + z f ) − (d + 0)and dynamic
ψ + zcharacteristic
of overgrazed grassland of northern
dh
h2 − h1
f −d
ity and the variable suction,
respectively.
q = K sat
= K sat
= K sat
= K sat f Argentina,
(I-1)Grassland, Breymeyer, A.,
Patagonia,
in:
Managed
dz assuming
z2 −dz1 is small in relazf −0
zf
Substituting in Eq. (A3) and
Elsevier Science, Amsterdam, 149–175, 1990.
tion to the other water potential terms:
Ares, J. O., del Valle, H. F., and Bisigato, A.: Detection of processin
which,
related changes in plant patterns at extended spatial scales durdF
θunsat − θi
ing early dryland desertification, Global Change Biol., 9, 1643–
INunsat =
= Kh q =ψinfiltration
+
1
,
(A6)
f
rate at saturated condition (mm/s),
dt
F
1659, 2003.
25
Ksat = saturated hydraulic conductivity (mm/s),
where θunsat is the unsaturated water content of the soil.
ψf = suction at wetting front (mm),
d = the depth of overland flow (mm).
Acknowledgements. This study was supported by grants of
Agencia Nacional de Investigaciones Cientı́ficas y Técnicas (ANPCyT) PICT 07-1738 and Consejo Nacional de Investigaciones
Cientı́ficas y Técnicas (CONICET) PIP 1142 0080 1002 01 to
J. O. Ares. M. J. Rossi was a doctoral fellow from ANPCyT during
2009–2012. An anonymous reviewer, S. Thompson and C. Harman
stimulated discussion on earlier versions of this paper.
Edited by: S. Thompson
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